cp's OEIS Frontend

A214900 Number of ordered ways to represent n as the sum of three squares and one fourth power.

%I A214900 #16 May 11 2019 17:51:54
%S A214900 1,4,6,4,4,9,9,3,3,9,12,9,4,7,12,6,4,15,18,10,12,18,12,3,6,18,27,19,5,
%T A214900 18,24,6,6,18,21,18,18,18,18,9,9,30,33,13,6,27,24,6,4,16,33,27,18,24,
%U A214900 33,12,12,27,18,18,12,24,30,12,4,30,45,21,18,33,30,6,12,21,33,34,10,27,30,6,9,40,39,24,25,33,39,18,9
%N A214900 Number of ordered ways to represent n as the sum of three squares and one fourth power.
%C A214900 Different orderings of summands are counted, e.g., 1 = 1^2 + 0^2 + 0^4 + 0^4 = 0^2 + 1^2 + 0^4 + 0^4 = 0^2 + 0^2 + 1^4 + 0^4 = 0^2 + 0^2 + 0^4 + 1^4, so a(1)=4.
%C A214900 Conjecture: a(n) != 0, that is, all numbers are sums of three squares and one fourth power.
%F A214900 G.f.: (Sum_{j>=0} x^(j^2))^3 * (Sum_{j>=0} x^(j^4)) (see PARI code).
%o A214900 (PARI)
%o A214900 N=10^3;  x='x+O('x^N);
%o A214900 S(e)=sum(j=0, ceil(N^(1/e)), x^(j^e));
%o A214900 v=Vec( S(4)^1 * S(2)^3 )
%Y A214900 Cf. A000925 (two squares), A002102 (three squares).
%K A214900 nonn
%O A214900 0,2
%A A214900 _Joerg Arndt_, Jul 29 2012